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Simplifying (42 + -1X)(X + 12) = 224 Reorder the terms: (42 + -1X)(12 + X) = 224 Multiply (42 + -1X) * (12 + X) (42(12 + X) + -1X * (12 + X)) = 224 ((12 * 42 + X * 42) + -1X * (12 + X)) = 224 ((504 + 42X) + -1X * (12 + X)) = 224 (504 + 42X + (12 * -1X + X * -1X)) = 224 (504 + 42X + (-12X + -1X2)) = 224 Combine like terms: 42X + -12X = 30X (504 + 30X + -1X2) = 224 Solving 504 + 30X + -1X2 = 224 Solving for variable 'X'. Reorder the terms: 504 + -224 + 30X + -1X2 = 224 + -224 Combine like terms: 504 + -224 = 280 280 + 30X + -1X2 = 224 + -224 Combine like terms: 224 + -224 = 0 280 + 30X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -280 + -30X + X2 = 0 Move the constant term to the right: Add '280' to each side of the equation. -280 + -30X + 280 + X2 = 0 + 280 Reorder the terms: -280 + 280 + -30X + X2 = 0 + 280 Combine like terms: -280 + 280 = 0 0 + -30X + X2 = 0 + 280 -30X + X2 = 0 + 280 Combine like terms: 0 + 280 = 280 -30X + X2 = 280 The X term is -30X. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30X + 225 + X2 = 280 + 225 Reorder the terms: 225 + -30X + X2 = 280 + 225 Combine like terms: 280 + 225 = 505 225 + -30X + X2 = 505 Factor a perfect square on the left side: (X + -15)(X + -15) = 505 Calculate the square root of the right side: 22.472205054 Break this problem into two subproblems by setting (X + -15) equal to 22.472205054 and -22.472205054.Subproblem 1
X + -15 = 22.472205054 Simplifying X + -15 = 22.472205054 Reorder the terms: -15 + X = 22.472205054 Solving -15 + X = 22.472205054 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + X = 22.472205054 + 15 Combine like terms: -15 + 15 = 0 0 + X = 22.472205054 + 15 X = 22.472205054 + 15 Combine like terms: 22.472205054 + 15 = 37.472205054 X = 37.472205054 Simplifying X = 37.472205054Subproblem 2
X + -15 = -22.472205054 Simplifying X + -15 = -22.472205054 Reorder the terms: -15 + X = -22.472205054 Solving -15 + X = -22.472205054 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + X = -22.472205054 + 15 Combine like terms: -15 + 15 = 0 0 + X = -22.472205054 + 15 X = -22.472205054 + 15 Combine like terms: -22.472205054 + 15 = -7.472205054 X = -7.472205054 Simplifying X = -7.472205054Solution
The solution to the problem is based on the solutions from the subproblems. X = {37.472205054, -7.472205054}
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